1. Field of the Invention
The present invention relates to a method of simulating a semiconductor device fabricating process or the like by a computer. More particularly, it relates to a method of simulating a diffusion of impurity when an interface is formed between a plurality of material regions.
2. Description of the Prior Arts
A process simulation means the simulation of a process of fabricating a semiconductor device. In the process simulation, without actually fabricating the semiconductor device, the semiconductor fabricating process such as an ion implantation process and a -diffusion process is analyzed by the use of a computer, whereby a physical amount and a shape such as impurity profile within the device are estimated. The process simulation is described in detail in Ryo Dan (author and editor), "Process Device Simulation Gijutsu (Process Device Simulation Technology)", pp. 18-29, April 1990, Sangyo Tosho Publishing Co., Ltd. A computer program for executing a process simulation is called a process simulator. Of the process simulators, the one for simulating a diffusion process is called a diffusion simulator. In general, the diffusion simulator executes the simulation of the diffusion process by numerical computation of a diffusion equation.
When a diffusion simulation is executed, more specifically, when the diffusion of the impurity is computed in a system in which two or more different material regions are in contact with one another, it is necessary to take a flux of the impurity on a material interface into consideration for the highly precise computation of an impurity concentration and also to adopt this flux into the diffusion equation. Heretofore, as described in C. P. Ho, J. D. Plummer, S. E. Hansen and R. W. Dutton, "VLSI Process Modeling-SUPREM III", IEEE Transactions on Electron Devices, Vol. ED-30, No. 11, pp. 1438-1453, November 1983, the flux of each impurity on the material interface has been defined, this flux has been adopted into the diffusion equation formulated with regard to each material region, simultaneous equations have been set up by the diffusion equation of each material region, and then the simultaneous equations have been solved.
In this method, as shown in FIG. 1, flux J(i) of a certain impurity i is first defined in certain coordinate points between material regions A and B, and then the value of the flux is determined. For example, the following equation is used. ##EQU1##
As the above equation (1), there is a method of determining flux J(i) by the use of a transport coefficient and a segregation coefficient on the interface. When the interface between material region A and material region B is assumed to be an A/B interface, h(i,A/B) represents the transport coefficient of impurity i on the A/B interface; m(i,A/B) represents the segregation coefficient of impurity i on the A/B interface; C(i,A) represents the concentration of impurity i on the A/B interface on the side of material region A; and C(i,B) represents the concentration of impurity i on the A/B interface on the side of material region B. This flux J(i) is used so as to determine the fluxes of impurity i on the A/B interface that should be added to the respective diffusion equations as to material regions A and B. The fluxes are determined by equations (2) and (3). EQU J(i,A)=J(i) (2) EQU J(i,B)=-J(i) (3)
Flux J(i,A) is added to the diffusion equation as to material region A, while flux J(i,B) is added to the diffusion equation as to material region B. After that, the simultaneous equations are set up by the diffusion equations to which the impurity fluxes are added, and the simultaneous equations are solved, so that the impurity concentration is obtained.
However, the above-described conventional technique taking the impurity flux on the interface between different material regions into account has a problem as described below. That is, when one impurity in material region A is changed into plural types of impurity in material region B, for example, when, in material region B, some impurity atoms enter a replacement site (lattice site) while others enter an interstitial site, the conventional method cannot deal with such a situation. The reason why this problem occurs is that the above-mentioned conventional method can define only the interfacial flux of the same type of impurity.